Mankiw raises several important concerns (the limited government spending multiplier [I use m sub G = 1], endless budget deficits, whether [permanent] tax cuts would work better), but the most relevent environmental economic issue is where the money is spent (Is government spending too easy an answer?):
People don’t usually spend their money buying things they don’t want or need, so for private transactions, this kind of inefficient spending is not much of a problem. But the same cannot always be said of the government. If the stimulus package takes the form of bridges to nowhere, a result could be economic expansion as measured by standard statistics but little increase in economic well-being.
The way to avoid this problem is a rigorous cost-benefit analysis of each government project. Such analysis is hard to do quickly, however, especially when vast sums are at stake. But if it is not done quickly, the economic downturn may be over before the stimulus arrives.